Lexicographic product graphs Pm[Pn] are antimagic
نویسندگان
چکیده
منابع مشابه
Regular Graphs are Antimagic
In this note we prove with a slight modification of an argument of Cranston et al. [2] that k-regular graphs are antimagic for k ≥ 2.
متن کاملDense graphs are antimagic
An antimagic labeling of a graph with m edges and n vertices is a bijection from the set of edges to the integers 1, . . . ,m such that all n vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called antimagic if it has an antimagic labeling. A conjecture of Ringel (see [4]) states that every connected graph, but K2,...
متن کاملRegular bipartite graphs are antimagic
A labeling of a graph G is a bijection from E(G) to the set {1, 2, . . . , |E(G)|}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling. In 1990, Ringel conjectured that every connected graph other than K2 is antimagic...
متن کاملLexicographic Product of Extendable Graphs
Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...
متن کاملRegular Graphs of Odd Degree Are Antimagic
An antimagic labeling of a graph G with m edges is a bijection from E(G) to {1, 2, . . . ,m} such that for all vertices u and v, the sum of labels on edges incident to u differs from that for edges incident to v. Hartsfield and Ringel conjectured that every connected graph other than the single edge K2 has an antimagic labeling. We prove this conjecture for regular graphs of odd degree.
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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2018
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2017.10.005